if a is 40% less than b and c is 40% of the sum of a and b then by what percentage b is greater than c
Let's solve this down step by step:
1. A is 40% less than B: This means A = 0.6B (since 100% - 40% = 60%)
2. C is 40% of the sum of A and B: This means C = 0.4(A + B)
Now, substitute the value of A from step 1 into the equation for C:
C = 0.4(0.6B + B)
C = 0.4(1.6B)
C = 0.64B
To find the percentage by which B is greater than C:
(B - C) / C × 100%
= (B - 0.64B) / 0.64B × 100%
= 0.36B / 0.64B × 100%
= 56.25%
So, B is greater than C by 56.25%.
Let B = 100 (assumed value).
Since A is 40% less than B, we get A = 100 - 40 = 60.
Now, C is 40% of the sum of A and B,
so C = 40% of (60 + 100) = 40% of 160 = 64.
The percentage by which B is greater than C is
[(100 - 64) / 64] × 100 = (36/64) × 100 = 56.25%.
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